# rcspline.eval

##### Restricted Cubic Spline Design Matrix

Computes matrix that expands a single variable into the terms needed
to fit a restricted cubic spline (natural spline) function using the
truncated power basis. Two normalization options are given for
somewhat reducing problems of ill-conditioning. The antiderivative
function can be optionally created. If knot locations are not given,
they will be estimated from the marginal distribution of `x`

.

- Keywords
- regression, smooth

##### Usage

```
rcspline.eval(x, knots, nk=5, inclx=FALSE, knots.only=FALSE,
type="ordinary", norm=2, rpm=NULL, pc=FALSE,
fractied=0.05)
```

##### Arguments

- x
a vector representing a predictor variable

- knots
knot locations. If not given, knots will be estimated using default quantiles of

`x`

. For 3 knots, the outer quantiles used are 0.10 and 0.90. For 4-6 knots, the outer quantiles used are 0.05 and 0.95. For \(\code{nk}>6\), the outer quantiles are 0.025 and 0.975. The knots are equally spaced between these on the quantile scale. For fewer than 100 non-missing values of`x`

, the outer knots are the 5th smallest and largest`x`

.- nk
number of knots. Default is 5. The minimum value is 3.

- inclx
set to

`TRUE`

to add`x`

as the first column of the returned matrix- knots.only
return the estimated knot locations but not the expanded matrix

- type
`"ordinary"`to fit the function,`"integral"`to fit its anti-derivative.- norm
`0`to use the terms as originally given by Devlin and Weeks (1986),`1`to normalize non-linear terms by the cube of the spacing between the last two knots,`2`to normalize by the square of the spacing between the first and last knots (the default).`norm=2`

has the advantage of making all nonlinear terms beon the x-scale.- rpm
If given, any

`NA`

s in`x`

will be replaced with the value`rpm`

after estimating any knot locations.- pc
Set to

`TRUE`

to replace the design matrix with orthogonal (uncorrelated) principal components computed on the scaled, centered design matrix- fractied
If the fraction of observations tied at the lowest and/or highest values of

`x`

is greater than or equal to`fractied`

, the algorithm attempts to use a different algorithm for knot finding based on quantiles of`x`

after excluding the one or two values with excessive ties. And if the number of unique`x`

values excluding these values is small, the unique values will be used as the knots. If the number of knots to use other than these exterior values is only one, that knot will be at the median of the non-extreme`x`

. This algorithm is not used if any interior values of`x`

also have a proportion of ties equal to or exceeding`fractied`

.

##### Value

If `knots.only=TRUE`

, returns a vector of knot
locations. Otherwise returns a matrix with `x`

(if
`inclx=TRUE`

) followed by \(\code{nk}-2\) nonlinear terms. The
matrix has an attribute `knots`

which is the vector of knots
used. When `pc`

is `TRUE`

, an additional attribute is
stored: `pcparms`

, which contains the `center`

and
`scale`

vectors and the `rotation`

matrix.

##### References

Devlin TF and Weeks BJ (1986): Spline functions for logistic regression modeling. Proc 11th Annual SAS Users Group Intnl Conf, p. 646--651. Cary NC: SAS Institute, Inc.

##### See Also

##### Examples

```
# NOT RUN {
x <- 1:100
rcspline.eval(x, nk=4, inclx=TRUE)
#lrm.fit(rcspline.eval(age,nk=4,inclx=TRUE), death)
x <- 1:1000
attributes(rcspline.eval(x))
x <- c(rep(0, 744),rep(1,6), rep(2,4), rep(3,10),rep(4,2),rep(6,6),
rep(7,3),rep(8,2),rep(9,4),rep(10,2),rep(11,9),rep(12,10),rep(13,13),
rep(14,5),rep(15,5),rep(16,10),rep(17,6),rep(18,3),rep(19,11),rep(20,16),
rep(21,6),rep(22,16),rep(23,17), 24, rep(25,8), rep(26,6),rep(27,3),
rep(28,7),rep(29,9),rep(30,10),rep(31,4),rep(32,4),rep(33,6),rep(34,6),
rep(35,4), rep(36,5), rep(38,6), 39, 39, 40, 40, 40, 41, 43, 44, 45)
attributes(rcspline.eval(x, nk=3))
attributes(rcspline.eval(x, nk=5))
u <- c(rep(0,30), 1:4, rep(5,30))
attributes(rcspline.eval(u))
# }
```

*Documentation reproduced from package Hmisc, version 4.3-1, License: GPL (>= 2)*